Solve 2-7u^25u^26u^2

Question

Simplify the expression

2 - 210 u^{6}

Evaluate

2 - 7 u^{2} \times 5 u^{2} \times 6 u^{2}

Solution

More Steps

Evaluate

7 u^{2} \times 5 u^{2} \times 6 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 5 \times 6

Multiply the terms

35 \times 6

Multiply the numbers

210

210 u^{2} \times u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

210 u^{2 + 2 + 2}

Add the numbers

210 u^{6}

2 - 210 u^{6}

Show Solution

Factor the expression

2 (1 - 105 u^{6})

Evaluate

2 - 7 u^{2} \times 5 u^{2} \times 6 u^{2}

Multiply

More Steps

Evaluate

7 u^{2} \times 5 u^{2} \times 6 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 5 \times 6

Multiply the terms

35 \times 6

Multiply the numbers

210

210 u^{2} \times u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

210 u^{2 + 2 + 2}

Add the numbers

210 u^{6}

2 - 210 u^{6}

Solution

2 (1 - 105 u^{6})

Show Solution

Find the roots

u_{1} = - \frac{6 10 5 ^{5}}{105}, u_{2} = \frac{6 10 5 ^{5}}{105}

Alternative Form

u_{1} \approx - 0.4604, u_{2} \approx 0.4604

Evaluate

2 - 7 u^{2} \times 5 u^{2} \times 6 u^{2}

To find the roots of the expression,set the expression equal to 0

2 - 7 u^{2} \times 5 u^{2} \times 6 u^{2} = 0

Multiply

More Steps

Multiply the terms

7 u^{2} \times 5 u^{2} \times 6 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 5 \times 6

Multiply the terms

35 \times 6

Multiply the numbers

210

210 u^{2} \times u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

210 u^{2 + 2 + 2}

Add the numbers

210 u^{6}

2 - 210 u^{6} = 0

Move the constant to the right-hand side and change its sign

- 210 u^{6} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 210 u^{6} = - 2

Change the signs on both sides of the equation

210 u^{6} = 2

Divide both sides

\frac{210 u ^{6}}{210} = \frac{2}{210}

Divide the numbers

u^{6} = \frac{2}{210}

Cancel out the common factor 2

u^{6} = \frac{1}{105}

Take the root of both sides of the equation and remember to use both positive and negative roots

u = \pm 6 \frac{1}{105}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{105}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 1}{6 105}

Simplify the radical expression

\frac{1}{6 105}

Multiply by the Conjugate

\frac{6 10 5 ^{5}}{6 105 \times 6 10 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

6105 \times 6 10 5^{5}

The product of roots with the same index is equal to the root of the product

6 105 \times 10 5^{5}

Calculate the product

6 10 5^{6}

Reduce the index of the radical and exponent with 6

105

\frac{6 10 5 ^{5}}{105}

u = \pm \frac{6 10 5 ^{5}}{105}

Separate the equation into 2 possible cases

u = \frac{6 10 5 ^{5}}{105} u = - \frac{6 10 5 ^{5}}{105}

Solution

u_{1} = - \frac{6 10 5 ^{5}}{105}, u_{2} = \frac{6 10 5 ^{5}}{105}

Alternative Form

u_{1} \approx - 0.4604, u_{2} \approx 0.4604

Show Solution